Solve for 12 - h(7)
First find h(7)
h(7) = 7^2+3(7)-2
h(7) = 49 + 21 - 2
h(7) = 68
12 - 68 = - 56
12 - h(7) = -56.
I'm not sure if the question wants h(-56) as well, but just plug that in.
H(-56)=2966
hope this helps :)
Students in a classroom have eaten 20% of jellybeans from a jar. There are now only 100 jellybeans left! How many jellybeans were in the jar to begin with?
Using percentages we calculate in the beginning there were 125 jellybeans in the jar.
Let the number of jellybeans in the jar was x.
Now student ate 20% of the jellybeans.
Number of jellybeans students ate = 20% of x = 0.2x
Number of jellybeans left = x - 0.2x = 0.8x
But the number of jellybeans is given as 100.
Therefore 0.8x = 100
or, x = 100 /0.8 = 125
Hence there were 125 jellybeans in the jar.
The English word "percentage" derives from the Latin phrase "per centum," which means "by the hundred." Percentages are fractions with a denominator of 100.
In other words, that is a relationship where it is always assumed that the value of the whole is 100.
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The graph below plots the values of y for different values of x:
plot the ordered pairs 1, 8 and 2, 3 and 3, 0 and 4, 1 and 5, 2 and 6, 1
What does a correlation coefficient of −0.2 say about this graph?
x and y have a strong, positive correlation
x and y have a weak, positive correlation
x and y have a strong, negative correlation
x and y have a weak, negative correlation
A correlation coefficient is a numerical measure of some type of correlation, meaning a statistical relationship between two variables.
Hence, the correlation coefficient is [tex]-0.9[/tex], i.e., [tex]x[/tex] and [tex]y[/tex] have a strong, negative correlation
What is a correlation coefficient?
A correlation coefficient is a numerical measure of some type of correlation, meaning a statistical relationship between two variables.
The variables may be two columns of a given data set of observations, often called a sample or two components of a multivariate random variable with a known distribution.
As we know that the correlation coefficient is a measure of the strength of the straight line or linear relationship between two variables. Correlation coefficients are expressed as values between [tex]+1[/tex] and [tex]-1[/tex].
So,
[tex](1,8),(2,3),(3,0),(4,1),(5,2),(6,1)[/tex]
As per the Excel tools i.e., CORREL function the correlation coefficient is [tex]-0.9[/tex].
Hence, the correlation coefficient is [tex]-0.9[/tex], i.e., [tex]x[/tex] and [tex]y[/tex] has a strong, negative correlation.
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Find the largest area for a rectangle that is inscribed in a semicircle with radius 4 inches.
The area of the largest rectangle is 25 square units.
It is given that the radius of the semicircle is [tex]4[/tex].
It is required to inscribe a rectangle of maximum area.
Consider a rectangle of sides [tex]x[/tex], [tex]y[/tex] as shown in the given figure.
From the attached figure,[tex]AB=x[/tex], [tex]OB=r[/tex] and [tex]OB=\frac{y}{2}[/tex].
Now, in the triangle OAB, apply Pythagoras' theorem as,
[tex](OA)^{2}=(OB)^{2}+(AB)^2[/tex]
[tex]r^2=(\frac{y}{2} )^2+x^2\\\\[/tex]
[tex]16=\frac{y}{4}+x^2[/tex]
[tex]y^2=4(16-x^2)[/tex]
[tex]y=2\sqrt{16-x^2}[/tex]
So, the area of the rectangle will be,
Area,
[tex]A = 2x \times y[/tex]
= [tex]2x \times \sqrt{(16 - x^2)}[/tex]
Differentiate the area with respect to ,
[tex]A' = 2 \times \sqrt{(16 - x^2)} - 2x^2/(16 - x^2)[/tex]
Differentiate the area twice as,
When[tex]x = 0, y = 5[/tex] and when [tex]x = 5, y = 0[/tex], [tex]area = 0[/tex].
It implies that area is maximum when the value of x lies between 0 and 5.
This will occur where [tex]A'= 0[/tex].
⇒ [tex]2 \times \sqrt{(16 - x2) }- 2x^2/(16 - x^2) = 0[/tex]
⇒[tex]2 \times \sqrt{(16 - x^2)} = 2x^2/(16 - x^2)[/tex]
On simplification, we get,
⇒ [tex]2 \times (16 - x^2) = 2x^2[/tex]
⇒ [tex]16 - x^2 = x^2[/tex]
⇒ [tex]2x^2= 16[/tex]
⇒ [tex]x^2 = 16/2[/tex]
⇒ [tex]x = \sqrt{8}[/tex]
Now, [tex]y = \sqrt{(16 - x^2)}[/tex] becomes
⇒[tex]y = \sqrt{(16 - (\sqrt8)^2)}[/tex]
⇒ [tex]y = \sqrt{(16 - 8)}[/tex]
[tex]y =\sqrt{8}[/tex]
Maximum area = 2xy
[tex]=2(\sqrt{8)}(\sqrt{8})[/tex]
[tex]=16[/tex]
Therefore, the area of the largest rectangle is 16 square units.
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a course catalog for the open university of earth lists classes via a sequence of three numbers (chosen from 0 to 9) followed by three letters in english (chosen from a to z). how many courses can be given unique catalog numbers? choose the best answer.
17576000 courses can be given unique catalog numbers.
There are three numbers and three English letters.
Each of three numbers can be chosen from 0 to 9, so the ways to choose each number is = 10
So the total number to choose three numbers = 10*10*10 = 1000
Each of letters can be chosen from A to Z.
Number of choice for the each letter = 26
So, the outcomes of letter combination = 26*26*26 = 17576
Hence the total possible catalog numbers = 1000*17576 = 17576000
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mike discovered that the pool in his backyard is leaking slowly. the pool holds 15,478 gallons of water, and is leaking at a rate of 11 gallons per day. if mike does not replace the water that has leaked from the pool, how many gallons of water will remain in the pool after 91 days?
The pool will have 14, 477 gallons of water.
The amount of water that has leaked in 91 days = rate of leakage × number of days
Keep the values in formula
The amount of water that has leaked in 91 days = 11 × 91
Performing multiplication
The amount of water that has leaked in 91 days = 1001 gallons
Amount of water remaining after 91 days = total amount of water - the amount of water that has leaked in 91 days
Amount of water remaining after 91 days = 15,478 - 1001
Performing subtraction
Amount of water remaining after 91 days = 14, 477 gallons
Hence, after 91 days there will be 14, 477 gallons of water in the pool.
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whats the equation of a line that passes through the points
(12,12) and (20,6)
Can someone pls help me with this and show your work it would mean a lot
Using the angle of elevation formula, the distance between John and Fred from the building is 1.2m and 1.67m.
What is the angle of elevation?The angular relationship between the horizontal plane and the line of sight for an object above the horizontal.The angle of elevation is the angle created between the line of sight and the horizontal. The angle created is an angle of elevation if the line of sight is upward from the horizontal line.You may calculate the angle of elevation, for instance, by standing on the ground and looking up at the peak of a mountain.So, the distance of the building from John and Fred is:
Let, the height of the building be QR and the distance between the building and John and Fred be PR and SR.Now, we get the formula:
Tanθ = QR/PRTanθ = QR/SRCalculate as follows:
John's distance:
Tanθ = QR/PR25 = 30/PRPR25 = 30PR = 30/25PR = 6/5Fred's distance:
Tanθ = QR/SR18 = 30/SRSR18 = 30SR = 30/18SR = 15/9SR = 1.67mTherefore, using the angle of elevation formula, the distance between John and Fred from the building is 1.2m and 1.67m.
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based on the graph what is the rate of the change for an airplane approaching an airport for landing
Answer:
(8, 9 000)
Step-by-step explanation:
Decide whether events A and B are overlapping or non-overlapping, you roll a red die and a blue die. event a is that you get a sum of 9. event b is that you get a double.() overlapping ()non-overlapping
Events A and B are non-overlapping. Option(2) is correct.
When two sets A and B have at least one element in common, they are said to be overlapping.
The sets of photographs that don't overlap are the sets where no two pictures (correctly) don't overlap. They are the expansion of the cross-bifix-free sets of strings to two dimensions is called non-overlapping.
A red die and a blue die are rolled.
Assume that Event A is receiving the number 9.
Event B: You receive a double.
Whether events A and B overlap or not is what we want to determine.
When two red dice and two blue dice are thrown, a sample space is then provided by,
S = {(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (3,1), (3,2), (3,3), (3,4), (3,5),(3,6), (4,1), (4,2), (4,3), (4,4),(4,5),(4,6) (5,1), (5,2), (5,3), (5,4),(5,5),(5,6),(6,1), (6,2),(6,3)(6,4),(6,5),(6,6)}
The two dice are rolled, and there are a total of 36 outcomes.
n(S)=36
Assume that Event A is receiving the number 9.
The probable results for A = (3,6), (4,5), (5,5), (5,6), (6,3)
And let's say that you receive a double in Event B.
The events that may occur if B=(1,1),(2,2),(3,3),(4,4),(5,5),(6,6)
We can observe that the two events are distinct from one another since there is no overlap in the potential outcomes of the two events.
Therefore events A and B are non-overlapping
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equivalent expressions
it’s due tmr and i don’t understand
thank you if you are willing to help
Answer:
c) x+4
Step-by-step explanation:
1. The original expression can be re-written as (I just rewrote each fraction so that there are no mixed numbers):
[tex]\frac{x}{2}+\frac{9}{2}+\frac{x}{2}-\frac{1}{2}[/tex]
2. Next, you want to group all the terms with the variable x, and all the terms without a variable. All the fractions should be rearranged:
[tex]\frac{x}{2}+\frac{x}{2}+\frac{9}{2}-\frac{1}{2}[/tex]
3. You can now simplify and add the variable terms and the non-variable terms.
[tex]\frac{x+x}{2}+\frac{9-1}{2}[/tex]
Simplify further:
[tex]\frac{2x}{2}+\frac{8}{2}[/tex]
[tex]x+4[/tex]
So your answer is choice c
This shows a linear function.
x y
0 15
1 25
2 35
3 45
4 55
Which equation represents the table?
A.
y = 10x + 15
B.
y = 15x + 10
C.
y = 10x
D.
y = 15x
Answer:
Option A: y = 10x + 15Step-by-step explanation:
Let's find the equation in the form of y=mx+b that fits the data. m is the slope and b is the y-intercept (the value of y when x=0). Slope, m, the the Rise/Run of the line. It can be found by taking any two points from the table. Let's choose (0,15) and (2,35), although any two will work.
x y
0 15
1 25
2 35
3 45
4 55
(0,15) (2,35)
The Rise is the change in y: (35 - 15) = 20.
The Run is the change in x for the same points: (2 - 0) = 2
The slope is the Rise/Run = (20/2) or 10.
The equation has the form y = 10x + b.
Let's find b. Just enter any of the points in the above equation and solve for b. I'll choose (3,45).
y = 10x + b
45 = 10*(3) + b
b = 45 - 30
b = 15
[Note: since b is the value of y when x equals zero, we really didn't need to calculate b as we just did. There is a data point already that tells us the value of y when x = 0: (0,15)]
The equation is y = 10x + 15Option A: y = 10x + 15Add. Write your answer as a fraction or as a whole or mixed number.
2 8/9 + 5 5/9 =
The required answer in mixed number for a given operation is [tex]8\frac{4}{9}[/tex]
What are mixed numbers?
A whole number and a proper fraction are both expressed together as a mixed number. A number between any two whole numbers is typically represented by it.
Given, [tex]2\frac{8}{9} + 5\frac{5}{9}[/tex]
[tex]= \frac{(2*9)+8}{9} +\frac{(5*9)+5}{9}[/tex]
[tex]= \frac{18+8}{9} +\frac{45+5}{9}[/tex]
[tex]= \frac{26}{9} +\frac{50}{9}[/tex]
[tex]= \frac{26+50}{9} = \frac{76}{9} = 8\frac{4}{9}[/tex]
Hence, the required answer for the given term is [tex]8\frac{4}{9}[/tex] .
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2/5 of what is 2/3? i need so much help
The answer is 4/15
2/5 * 2/3 = 2 · 2/5 · 3 = 4/15
Multiply the numerators and denominators together. Keep the result fraction to the smallest possible denominator GCD(4, 15) = 1. It cannot further simplify the fraction result by canceling in the following intermediate step.
In other words, two fifths times two thirds equals four fifteenths.
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Answer:
5/3
Step-by-step explanation:
"of" means times so so so often. It is not a hard math rule/definition. But more like a soft English-Math translation.
So, "2/5 of what"
means 2/5x (but make sure the 2/5 is a fraction beside the x, NOT the x on the bottom with the 5)
"is" means equals.
2/5x = 2/3
Multiply both sides by 5/2.
5/2 • 2/5x = 2/3•5/2
x = 2/3 • 5/2
x = 5/3
You get 5/3 either by "cancelling" the 2's OR by
fraction multiplication where you times top×top and bottom×bottom and simplify.
x = 10/6
x = 5/3
2/5 of 5/3 is 2/3.
The "what" in the question is 5/3.
PLEASE HELP!!!!!!!!!!!!!
A handicapped ramp is being constructed for the front entrance of First National Bank in Springfield. ADA guidelines requires a rise angle from the foot of the ramp (point furthest from the entrance) not to exceed 4.8 degrees. This means the vertical to horizontal ratio cannot exceed 1:12. If the handicapped ramp must start 15 feet away from the front entrance, contractors estimate the rise to be about 3 feet.
Part A: Explain thoroughly whether or not these ramp dimensions meet the ADA guidelines.
Part B: If the rise estimate does not meet ADA requirements, provide a measurement that would meet the guidelines.
a) These ramp dimensions do not meet the ADA guidelines.
b) A measurement that would meet the guidelines is the ramp starting 39 feet away, with a height of 3 meters.
What is a slope?The slope of a situation is given by the vertical change divided by the horizontal change, and it's also the tangent of the angle of depression.
For the ramp in this problem, we have that the vertical change and the horizontal change are given as follows:
The vertical change is of: 3 feet.The horizontal change is of: 15 feet.The ratio between the vertical change to the horizontal change is of:
3/15 = 1/5.
Which is greater than 1/12, hence the ramp does not meet the ADA guidelines.
If the horizontal change was 13 times the vertical change, it would meet the ratio, hence a possible measurement is of:
3 feet vertical.39 feet horizontal.As the ratio would be of:
3/39 = 1/13 < 1/12.
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Encuentre dos números positivos cuyo producto es 25 y cuya suma es un mínimo. (Especifica el valor minimo y maximo si los dos valores no son lo mismo.)
The two positive numbers are 5 , 5.
Given:
Product of two positive numbers = 25
sum of these number is minimum.
Let a and b be the two positive numbers.
a*b = 25
b = 25/a
sum s = a+b
= a + 25/a
apply derivation on both sides.
ds/da = 1 - 25/[tex]a^{2}[/tex]= 0.
1 = 25/[tex]a^{2}[/tex]
a = [tex]\sqrt{25}[/tex]
a = 5 , -5
since given are positive numbers so 5 is considered.
b = 25/5
b = 5
Therefore the two positive numbers are 5 , 5.
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A railroad
car container can hold 42,000 pounds.
Mr. Evans wants to ship 90 ovens and
some freezers in the same container.
If each freezer weighs 600 pounds,
how many freezers could be shipped
in the container? Explain.
40 freezers could be shipped in the container.
What is a variable?
A variable is a quality that may be measured and take on several values.
We are given that
A railroad container can hold weight=42,000 pounds
Total number of ovens for ship=90
Weight of each oven=200 lbs
Weight of each freezer=600 pounds
We have to find the number of freezers that can be shipped in the container.
Let x be the number of freezers that can be shipped in the container.
According to the question,
42000=90(200)+600x
42000=18000+600x
600x=42000-18000=24000
x=24000/600=40
Hence, 40 freezers can be shipped in the container.
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Aiden ha $3 worth of dime and quarter. He ha 2 more dime than quarter. Determine the number of dime and the number of quarter that Aiden ha
The number of dime and the number of quarters that Aiden have are 10 and 8 respectively.
How to find the number of dime and quarter?Aiden ha $3 worth of dime and quarter. Aiden has 2 more dime than quarter. The number of dime and the number of quarter that Aiden has can be calculated as follows:
let
x = number of quarter
y = number of dime
Therefore,
y = 2 + x
y - x = 2
0.1y + 0.25x = 3
Multiply equation(ii) by 10
y - x = 2
y + 2.5x = 30
subtract equation(i) from equation(ii)
3.5x = 28
x = 28 / 3.5
x = 8
Hence,
y = 2 + 8
y = 10
Therefore,
number of dime = 10
number of quarters = 8
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What is the area of the parallelogram shown?
A= In^2
a salesman keeps 20% of his sales as a commission. how much does he have to sell to earn $1,000?
Answer:
He has to sell 5000 to earn $1000
Step-by-step explanation:
1000/0.2 = 5000
Justify each step of the solution by stating the property that was used to get to each step. (4 points - 1 point each correct answer)
Given: 2(10 - 13x) + 9x) = -34x + 60
Step 1: 20 + 26x + 9x = -34x + 60
Step 2: -17x = -34x + 40
Step 3: 17x = 40
Step 4: x = 40/17
Sample Answer
Step 1: _____ property
Step 2: ______ property
Step 3: ______ property
Step 4: ______ property
a group of five friends goes to the state fair. each friend pays the entrance fee and buys one booklet of ride tickets and a meal ticket. the entrance fee is d dollars. a booklet of ride tickets costs 2.5 times the entrance fee. a meal ticket costs $4 less than the entrance fee.
Answer: What do you need the total or the equation? I am going to write the equation.
Step-by-Step Solution: (5)(d)+(5)(d)(2.5)+ (5)(d)-4
What is this shape ?
Answer:
Decagon
Step-by-step explanation:
Because it has 10 sides.
Answer:
Its a Decagon
Step-by-step explanation:
During the problem disaggregation process, the logic trees should have branches that are?.
During the problem disaggregation process, the logic trees should have branches that are both mutually exclusive and collectively exhaustive.
Problem disaggregation refers to the process of breaking down the larger higher-level operation into smaller plans and shorter periods. It refers to the use of analysis, logic, and facts to evaluate and understand each element of the problem in terms of causes and driver of the situation using logic trees. Logic trees improve the problem definition and aid in understanding an issue in more detail. There are different types of logic trees used in the process – factor logic tree, inductive logic tree, deductive logic tree, hypothesis tree, and decision tree. The logic trees should have branches that are MECE – mutually exclusive and collectively exhaustive. It is the second and an important step in the seven steps bulletproof problem-solving process used for complex solving.
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Equation of a line in point- slope form, that passes through (1,-7) and has a slope of -2/3?
The equation of a line in point- slope form, that passes through (1, -7) and has a slope of -2/3 is (y + 7) = -2/3 (x - 1)
How to determine the equation of a line in point- slope formInformation gotten from the question include
a slope of -2/3
points (1, -7)
What is linear function ?A linear function consists of functions where the variables has exponents of 1.
The equation of a line in point- slope form is expressed in the form.
(y - y₁) = m (x - x₁)
Definition of variables
(y and y₁) = refers to variables in the y direction
m = slope
x and x₁ = refers to variables in the x direction
substituting into the slope and point (1, -7) equation gives
()y + 7) = -2/3 (x - 1)
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A youth group is planning a trip to a local amusement park. They are taking a van which holds 10 people. It will cost $25 for parking and tickets to enter the park are $18 per person. Create a table to represent the situation, showing the possible total costs for the various numbers of people who could go?
What is the value of y?
y =
Find the following angle measures.
mAngleJKM = °
mAngleMKL = °
Applying the definition of linear pair angles, the measures are:
y = 10
m∠JKM = 106°
m∠MKL = 74°
What is the Linear Pair?A linear pair involves two angles that lie adjacent to each other on a straight line. The sum of their measures is equal to 180 degrees, this is because linear pair angles are supplementary to each other.
Given the following:
Measure of angle JKM = (10y + 6)°
Measure of angle MKL = (8y - 6)°
Therefore:
m∠JKM + m∠MKL = 180 [linear pair angles are supplementary]
Substitute
10y + 6 + 8y - 6 = 180
Combine like terms
18y = 180
18y/18 = 180/18
y = 10
Plug in the value of y to find the measures:
Measure of angle JKM = (10y + 6)° = 10(10) + 6 = 106°
Measure of angle MKL = (8y - 6)° = 8(10) - 6 = 74°
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The cost of the Gas is 11p for each unit
there is also a fixed charge of £25.57
calculate the cost of the gas
you must show your working
The cost of the gas will be equal to £67.81 p.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that,
Initial gas reading = 8247
Final gas reading = 8631
The total consumed gas is given by,
Final gas reading - Initial gas reading → 8631 - 8247 = 384
Since the cost of gas is 11p per unit we have, the total cost of the gas consumed is given by
Cost of consumed gas = Units of gas consumed × Unit cost of gas
= 384 × 11p = 4224 p
100 p ≡ £ 1
4224 p = £42.24 p
The total cost of the gs is obtained by adding the fixed charge to the cost of gas consumed as follows,
£25.57 + £42.24 = £67.81 p
The cost of the gas = £67.81 p
The complete question is given below,
The gas meter readings at the beginning and end of a period were: 8247 = 8631 the cost of the gas is 11p for each unit. there is also a fixed charge of £25.57. calculate the cost of the gas. you must show your working
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Stacy bought 8.3 pounds of fruit for a class party. The class ate 7.44 pounds of the fruit. How much fruit is left?
Answer:
0.86 pounds of fruit is left.
Step-by-step explanation:
If Stacey bought 8.3 pounds and the class ate 7.44 pounds, the amount of fruit that's left is 8.3-7.44=0.86
Write the number below as a fraction in its simplest form
0.538
Answer:
0.538 as a fraction in its simplest form is 269/500
Step-by-step explanation:
We all know that 0.538 can be written as 0.538/1
Multiply the numerator and denominator by 1000 which comes out to 538/1000
Divide the numerator and denominator by 2 which comes out to 269/500
Since 269 is a prime number 269/500 is 0.538 in its simplest form
How much water must be added to 14 liters of a 90%
acid solution to obtain a 40% acid solution?
17.5 litres of must be added to 14 litres of a 90% acid solution to obtain a 40% acid solution.
What is percentage?A percentage is a number or ratio expressed as a fraction of 100.
Given that, there are 14 litres of a solution which is 90% acidic,
Let water added be x, then according to question,
0.90*14 = 0.40(x+14)
12.6 = 0.40x + 5.6
0.40x = 7
x = 17.5
Hence, 17.5 litres of must be added to 14 litres of a 90% acid solution to obtain a 40% acid solution.
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